Equations for potential annual direct incident radiation

and heat load

I have published two papers on this topic. The purpose of both is to estimate potential direct incident radiation (PDIR) and heat load from latitude, slope, and aspect. The limitations of these methods are described in the associated papers, but they provide convenient methods for estimating these values for a large number of points on a landscape. You can download associated data files from the links below.

The earlier paper (2002) used least-squares multiple linear regression of trigonometric functions. This method is still useful but the fit is not as good as with the method presented in the later paper (2007). The later paper uses a multiplicative kernel smoother which provides excellent interpolation.

McCune, B. 2007. Improved estimates of incident radiation and heat load using non-parametric regression against topographic variables. Journal of Vegetation Science 18:751-754.
Download pdf.
Download Appendices 1 and 2.

Files needed for NPMR. These are spreadsheets structured for HyperNiche.

   Northern hemisphere  Southern hemisphere
833 rows x 1 column
833 rows x 1 column
 Heat load HeatLoad-N.wk1
833 rows x 1 column
833 rows x 1 column
 Topographic variables LatSlopeAspect360.wk1
833 rows x 3 columns
833 rows x 3 columns
(same as for N hemisphere)
 Model specification file for HyperNiche BestLLModel.spx
BestHeatloadLLmodel.spx (same model file for both PDIR and Heat load, but response variable has a different name)
This is a binary file, so choose "Save" rather than "Open".
(same as for N hemisphere)
This is a binary file, so choose "Save" rather than "Open".

(The spreadsheets for the northern hemisphere can also be downloaded as text-based *.csv format spreadsheets: PDIR-N.csv, HeatLoad-N.csv, LatSlopeAspect360.csv)

Row names in these files follow the convention: Rows for aspects from 0-180 degrees east of north are named ObsE1, ObsE2, etc. Rows for aspects from 180-360 degrees east of north are named ObsW1, ObsW2, etc.

In HyperNiche, generate estimates for new points on the landscape with the following steps:

1. Create a spreadsheet with row (point) names, plus three data columns named lat, slope, aspect (all lower case). Note that all angles must be in the domain 0-360 degrees. Convert the data to degrees, if not already in those units. Save as a *.wk1 file.
2. In HyperNiche, open the appropriate PDIR or heat load file as the response matrix.
3. Open the model specification file (File | Open | Model file | BestLLModel.spx).
4. Open the file LatSlopeAspect360 as the predictor matrix.
5. Select Prediction | New sites and select the file you prepared in step 1. Select other options as desired. The resulting estimates will be written into the result file and/or a spreadsheet, as you choose.

The differences between the values for the northern and southern hemispheres are explained in a supplemental document, NvsS.pdf.

McCune, B. and D. Keon. 2002. Equations for potential annual direct incident radiation and heat load. Journal of Vegetation Science 13:603-606. Download pdf.

Download spreadsheet (testrad.xls) with equations and test data.

Sean Parks created a automated ArcView GIS script to calculate the Heat Load
Index describe in this paper. He has placed it on the ESRI script download website so that others may use it. See http://arcscripts.esri.com/ and search on "heat load" or http://arcscripts.esri.com/details.asp?dbid=13368

Download pdf for adjustments to use for southern hemisphere (Hemispheres.pdf). Updated 4 Oct 2004.

Errata for McCune & Keon (2002):

1. In the Excel equation on p. 605, the last term of the first line
should be -1.5*COS(I3), not -1.*COS(I3)

2. In Table 2, p. 605, the third to last value in the "Eq. 1" column
should be -0.984, not -0.939.